This study develops an integer linear programming (ILP) model for make-or-buy decisions in a make-to-order (MTO) manufacturing environment with a flexible job shop configuration. Regarding the decision to self-produce, specifically, the proposed model specifies the production plan, including resource allocation, and considers the penalty cost for tardiness. By contrast, the mathematical model indicates when the decision to outsource is made by a robust analysis. This study aims to minimize total overtime, subcontracting, and delay costs. A case study in the packaging industry is used to demonstrate the efficiency of the proposed model. The results indicate an optimal production plan with the planned number of production orders on the machine as well as the use of the machine in shifts. In addition, a sensitivity analysis shows the impact of cost-related parameters on alternative production planning options. This study contributes an effective optimization model to a complex real-world problem.